Chapter 4.4, Problem 2ES

a.

To determine

To approximate: The value of the integral ${\displaystyle \underset{-0.5}{\overset{0.5}{\int }}{\cos }^{2}x}dx,n=4$ using the complex trapezoidal rule.

b.

To determine

To approximate: The value of the integral ${\displaystyle \underset{-0.5}{\overset{0.5}{\int }}x\ln \left(x+1\right)dx},n=6$ using the complex trapezoidal rule.

c.

To determine

To approximate: The value of the integral ${\displaystyle \underset{0.75}{\overset{1.75}{\int }}\left({\sin }^{2}x-2x\sin x+1\right)dx},n=8$ using the complex trapezoidal rule.

d.

To determine

To approximate: The value of the integral ${\displaystyle \underset{e}{\overset{e+2}{\int }}\frac{1}{x\ln x}dx},n=8$ using the complex trapezoidal rule.